Patent application title: Method and Apparatus for the Stabilization of Spectrometric Transducers

Abstract:

The invention provides a method for stabilising a spectrometric
transducer for an optical spectrum measuring instrument by obtaining an
instantaneous central wavelength of a thermally controlled tunable filter
of the instrument, calibrating for a selected ambient temperature,
determining a heat variance of the filter and controlling the filter to
compensate for heat variance.

Claims:

1. A method for stabilizing a spectrometric transducer for an optical
spectrum measurement instrument, comprising: obtaining an instantaneous
central wavelength of a thermally controlled tunable filter of the
instrument; calibrating for a selected ambient temperature; determining a
heat variance of the filter; and controlling the filter to compensate for
the heat variance.

Description:

[0001] This application is a continuation of U.S. patent application Ser.
No. 12/318,040 filed on Dec. 19, 2008 which is a continuation of U.S.
patent application Ser. No. 11/754,781 filed on May 29, 2007 which is a
continuation of U.S. patent application Ser. No. 11/038,490 filed on Jan.
21, 2005 which claims priority from U.S. Provisional Patent Application
No. 60/537,919 filed on Jan. 22, 2004.

FIELD OF THE INVENTION

[0002] The present invention relates to a method for the stabilization of
spectrometric transducers.

BRIEF DESCRIPTION OF THE DRAWINGS

[0003] An embodiment of the present invention will now be described by way
of example only with reference to the accompanying drawings, in which:

[0004] FIG. 1 is a schematic diagram of an optical spectrum measurement
instrument.

[0005] FIG. 2 is a schematic representation of a portion of the apparatus
shown in FIG. 1.

[0006] FIG. 3 is a flow diagram of a thermal stabilization method for a
spectrometric transducer.

[0007] FIG. 4 is a plot showing the variation of controlling current for a
particular set of parameters.

DETAILED DESCRIPTION OF THE INVENTION

[0008] In FIG. 1 there is shown an optical spectrum measurement instrument
20 for analyzing optical signal 12. The optical signal 12 is sampled by
sampler 14, which provides optical spectrum **16 to the optical spectrum
measurement instrument 20. The optical spectrum measurement instrument 20
includes spectrometric transducer 30, including a tunable filter 32 and
photodiode 34, and Digital Signal Processor (DSP) 40. Optical spectrum
χ(λ) 16 is separated into its optical components by tunable
filter 32, after which its components are converted from optical to
current by photodiodes 34, resulting in an electrical spectrometric data
representation y(t) 36 of optical spectrum χ(λ) 16. The
spectrometric data representation y(t) 36 is then used by the DSP 40 to
compute an estimate χ(λ) 42 of the optical signal 12 optical
spectrum, which is then provided to user display 50. Optionally, the DSP
40 may also compute various parameters relating to the optical signal 12
optical spectrum such as power measurements, OSNR, BER, etc. or may
implement signal analysis or reconstruction algorithms. The response of a
filter to an input optical signal whose spectrum is χ(λ) 16,
i.e. the output current of the photodiode 34, may be modelled by an
integral operator of the form:

where λ is wavelength, t is time, g(λ, t) is the filter
response function, and Fy[] is a slightly nonlinear scalar function
of a scalar variable. For a monochromatic input signal, whose spectrum is
χ(λ)=δ(λ-1), this model responds with:

[0009] The response g(1, t), defined by Equation 2, is a gaussoid-like
function with a maximum changing monotonically with the wavelength 1. The
function of time g0(t), defined by Equation 3, characterizes the
amplitude variability of the filter response along the wavelength axis.

[0010] As shown in FIG. 2, the instantaneous central wavelength of the
filter is externally controlled by the current i(t) 38. In the preferred
embodiment, the filter 32 is a thermally controlled filter in which the
central wavelength depends on its internal temperature. The current i(t)
38 drives a variable resistance heater incorporated in the filter. Such
filters utilize the characteristic that as the temperature on tunable
filters varies, such as a particular optical material's change in its
index of refraction n with temperature T, so its center wavelength
varies, resulting in thermally-controlled tunable filters. The
temperature of the filter depends on the heat supplied from the
resistence heater and the heat loss/gain to/from the ambient environment.
To compensate for the heat loss/gain, a signal containing information
about the ambient temperature is used to compensate the current i(t) 38
supplied to the heater. The current is adjusted by the controller that
implements a control algorithm to maintain the filter at the desired
center frequency.

[0011] Assume that the function λ=F0 (u) is the result of
wavelength calibration for a selected ambient temperature T0
represented by the voltage U0. Assume, moreover, that the input
signal is generated by a battery of lasers whose central wavelengths are
uniformly distributed in the interval [λmin, λmax]:

[0012] Then, the maxima y0,jmax of the response of the
stabilized filter to such a signal may be easily identified together with
the corresponding values of the voltage
u(t):u0,j=F0-1(λj) for j=1, . . . , J. The
practical purpose of controlling the current i(t) 38 may be now
formulated as follows. For an arbitrary ambient temperature T, find i(t)
such that the maxima of the stabilized filter response remain as close as
possible to the maxima determined for T0 , i.e. the coordinates of
the maxima for the ambient temperature T, the values u1, . . . ,
uJ of the voltage u(t) and the values y1max, . . . ,
yJmax of the output signal y(t), satisfy the condition:

[0013] The task of control may be significantly simplified (at the price
of the sub-optimality of the solution) by an appropriate parameterization
of the heating current i(t). An example of such a parameterization is
defined by the formula:

where i1, i2, i3, t2 and t3 are parameters of
the current to be optimized by minimization of the left-hand side of
Equation 5. The parameterization of controlled current enables one to use
an empirical procedure of optimization that does not require any explicit
reference to the mathematical model of the stabilized filter. This
procedure is implemented in the controller and is depicted by the flow
chart shown in FIG. 3. The sequence of steps composing the procedure is
indicated by the sequence of blocks 62 to 70.

[0014] In block 62, for the selected ambient temperature T0, the
values of i1, i2, i3, t2 and t3 are chosen so as
to produce a relatively uniform distribution of
u0,j=F0-1(λj) for j=1, . . . , J.

[0015] Then in block 64, on the basis of measurements performed for the
same ambient temperature, the matrix Sy, of the sensitivity of the
maxima y1max, . . . , yJmax is computed for a small
change in the ambient temperature ΔT and for small changes
Δi1, Δi2, Δi3, Δt2 and
Δt3 in the parameters i1, i2, i3, t2 and
t3.

[0016] Similarly, in block 66, on the basis of measurements performed for
the same ambient temperature, the matrix Su of the sensitivity of
the corresponding maxima voltage values u1, . . . , uJ to is
computed for a small change in the ambient temperature ΔT and for
small changes Δi1, Δi2, Δi3,
Δt2 and Δt3 in the parameters i1, i2,
i3, t2 and t3 .

with respect to Δi1, Δi2, Δi3,
Δt2 and Δt3 for an assumed (sufficiently small)
increment ΔT of the ambient temperature.

[0018] Following which, in block 70, the ambient temperature is changed to
the value T=T0+ΔT; the new values of i1, i2,
i3, t2 and t3 are computed using increments
Δi1, Δi2, Δi3, Δt2 and
Δt3 determined in block 68; i1, i2, i3, t2
and t3 are empirically corrected in such away as to satisfy the
condition defined by Equation 5.

[0019] Finally, blocks 62 to 70 are repeated iteratively as to cover the
whole range of ambient temperatures the stabilized filter is assumed to
operate in.

[0020] It should be noted that the whole process of optimization is
subject to the constraint concerning the admissible values of current and
heating time.

[0021] A further refinement of the thermal stabilization of the stabilized
filter is possible during the software pre-processing of the data
provided by the stabilized filter using the above described hardware
means. The residual instabilities may be characterized during general
calibration of the stabilized filter, and the results of this
characterization may next be used for correction of the raw data before
their pre-processing.

[0022] A closer empirical study of the current i(t) control based on
Equation 6 provides the following: [0023] t2 and t3 may be
fixed to the values 1 ms and 5 ms, respectively; [0024] abrupt changes of
current i(t) should be avoided; [0025] a convex control in the interval
[t2, t3] would be desirable.

[0026] Consequently, a second example of the current i(t) parameterization
may been designed. It is defined by the formula:

and c1=I0, c2=I1. An example of the current i(t)
generated according to the above formula is shown in FIG. 4 and
I0=100 mA, I1=50 mA, I3=120 mA, and I5-150 mA.

[0028] The components of a spectrometer or the device in which it is used
such as an OPM are subject to aging. Consequently, the parameters of the
OPM drift in time. In particular, the absolute accuracy of wavelength
estimation is deteriorating. Taking into account that the contemporary
DWDM transmitters contain highly stable lasers, one may use the time
series of wavelength estimates as the basis for compensation of the time
drift of the OPM.

[0029] The idea of using time series of wavelength estimates provided by
the OPM for time drift compensation of this OPM is based on an assumption
that the average deviation of the central wavelength of the laser signal
used for this purpose is close to zero, i.e. there is no systematic
evolution of this wavelength over time. Consequently, the average
deviation of the central wavelength as computed by the OPM should be
expected to also be close to zero. If not, this average deviation may be
used to model the OPM's drift and provide a way of stabilizing the OPM by
compensating for this time drift.

[0030] A wavelength such as described above may be modelled by means of a
stochastic process:

l(t)=i+δl(t) Equation 11

where t is time, i is the central wavelength value according to the ITU
grid, and δl(t) is a stochastic process modelling the wavelength
deviation from the ITU-grid value. The latter process is assumed to be
zero-mean and stationary. Consequently, the time sampling of l(t) at
equidistant time points, t1, . . . , tN, yields the vector of
random variables:

where Δl(tn) is the time drift of wavelength to be estimated
on the basis of the realizations {circumflex over (l)}(tn) of the
random variables {circumflex over (l)}(tn). The vector {circumflex
over (l)}=.left brkt-bot.{circumflex over (l)}(t1) . . . {circumflex
over (l)}(tN).right brkt-bot.T has the following statistical
properties:

[0032] Assuming that the solution is to be approximated by a linear
combination:

Δ l ( t ) = j = 1 J p j
Φ j ( t ) Equation 16 ##EQU00011##

of known functions δj(t), such as, for example, a polynomial,
an orthogonal polynomial, a trigonometric polynomial, a b-spline, etc,
with unknown coefficients pj forming the vector p=[pi . . .
pJ]T. This vector is to be estimated on the basis of the
approximate equations:

[0035] If the samples may be considered uncorrelated, then estimates
{circumflex over (p)}j, . . . , {circumflex over (p)}K of the
parameters pJ, . . . , pK, characterizing the drift of K DWDM
channels, may be obtained using the LS method, described in the previous
section, in an integrated numerical process:

where Δ{circumflex over (l)}K is the vector of deviations of
the results of measurements of the central wavelength in the kth channel
from the ITU-grid value of this wavelength. In general, the channels may
differ in the laser wavelength deviation; the corresponding variances
σ12, . . . σK2 may be estimated according
to the formula:

[0036] Then the uncertainty-based weighing may be applied to obtain the
solution:

p = k = 1 K 1 σ k 2 p ^ k k =
1 K 1 σ k 2 Equation 26 ##EQU00015##

characterizing the wavelength-averaged drift of the OPM over time.

[0037] If the maximum deviation of the central wavelength of the laser
signal used for the OPM drift compensation is negligible with respect to
the assumed maximum error of wavelength measurements performed by the
OPM, then the time drift of the OPM may be corrected on the basis of a
single result of measurement.

[0038] As well, if the standard deviation of the central wavelength
averaged over a time interval ΔT is negligible with respect to the
assumed standard deviation of the error of wavelength measurements
performed by the OPM, and the OPM drift during the time interval ΔT
is negligible, then the time drift of OPM may be corrected on the basis
of the average of results of measurement performed during ΔT.

[0039] Although the present invention has been described by way of a
particular embodiment and examples thereof, it should be noted that it
will be apparent to persons skilled in the art that modifications may be
applied to the present particular embodiment without departing from the
scope of the present invention.